A hybrid Cartesian grid/gridless method is developed for calculating viscous flows over multi-element airfoils.The method adopts an unstructured Cartesian grid to cover most areas of the computational domain and leave...A hybrid Cartesian grid/gridless method is developed for calculating viscous flows over multi-element airfoils.The method adopts an unstructured Cartesian grid to cover most areas of the computational domain and leaves only small region adjacent to the aerodynamic bodies to be filled with the cloud of points used in the gridless methods,which results in a better combination of the computational efficiency of the Cartesian grid and the flexibility of the gridless method in handling complex geometries.The clouds of points in the local gridless region are implemented in an anisotropic way according to the features of the thin boundary layer of the viscous flows over the airfoils,and the clouds of points at the vicinity of the interface between the grid and the gridless regions are also controlled by using an adaptive refinement technique during the generation of the unstructured Cartesian grid.An implementation of the resulting hybrid method is presented for solving two-dimensional compressible Navier-Stokes(NS)equations.The simulations of the viscous flows over a RAE2822airfoil or a two-element airfoil are successfully carried out,and the obtained results agree well with the available experimental data.展开更多
A preconditioned gridless method is developed for solving the Euler equations at low Mach numbers.The preconditioned system in a conservation form is obtained by multiplying apreconditioning matrix of the type of Weis...A preconditioned gridless method is developed for solving the Euler equations at low Mach numbers.The preconditioned system in a conservation form is obtained by multiplying apreconditioning matrix of the type of Weiss and Smith to the time derivative of the Euler equations,which are discretized using agridless technique wherein the physical domain is distributed by clouds of points.The implementation of the preconditioned gridless method is mainly based on the frame of the traditional gridless method without preconditioning,which may fail to converge for low Mach number simulations.Therefore,the modifications corresponding to the affected terms of preconditioning are mainly addressed.The numerical results show that the preconditioned gridless method still functions for compressible transonic flow simulations and additionally,for nearly incompressible flow simulations at low Mach numbers as well.The paper ends with the nearly incompressible flow over a multi-element airfoil,which demonstrates the ability of the method presented for treating flows over complicated geometries.展开更多
The least-square gridless method was extended to simulate the compressible multi-material flows. The algorithm was accomplished to solve the Arbitrary Lagrange-Euler( ALE) formulation. The local least-square curve fit...The least-square gridless method was extended to simulate the compressible multi-material flows. The algorithm was accomplished to solve the Arbitrary Lagrange-Euler( ALE) formulation. The local least-square curve fits was adopted to approximate the spatial derivatives of a point on the base of the points in its circular support domain,and the basis function was linear. The HLLC( Harten-Lax-van Leer-Contact) scheme was used to calculate the inviscid flux. On the material interfaces,the gridless points were endued with a dual definition corresponding to different materials. The moving velocity of the interface points was updated by solving the Riemann problem. The interface boundary condition was built by using the Ghost Fluid Method( GFM).Computations were performed for several one and two dimensional typical examples. The numerical results show that the interface and the shock wave are well captured,which proves the effectiveness of gridless method in dealing with multi-material flow problems.展开更多
The gridless method coupled with finite rate chemistry model is employed to simulate the external combustion flow fields of M864 base bleed projectile. The fluid dynamics process is described by Euler Equation in 2-D ...The gridless method coupled with finite rate chemistry model is employed to simulate the external combustion flow fields of M864 base bleed projectile. The fluid dynamics process is described by Euler Equation in 2-D axisymmetric coordinate. The numerical method is based on least-square gridless method,and the inviscid flux is calculated by multi-component HLLC( Harten-Lax-van Leer-Contact) scheme,and a H2-CO reaction mechanism involving 9 species and 11 reactions is used. The computations are performed for the full projectile configuration of Ma = 1. 5,2,and 3. The hot air injection cases and inert cases are simulated for comparison. The numerical results show that due to the combustion in the weak region,the recirculation zone enlarges and moves downstream,the base pressure increases and the total drag force coefficient decreases. At Ma = 3. 0,the rear stagnation point shifts downstream approximate 0. 26 caliber,and the base pressure increases about 53. 4%,and the total drag force coefficient decreases to 0. 182 which agrees well with the trajectory model prediction. Due to neglecting the effects of viscosity and turbulence,there exists a certain difference at Ma = 1. 5,2. 0.展开更多
In this paper,preconditioned gridless methods are developed for solving the threedimensional(3D)Euler equations at low Mach numbers.The preconditioned system is obtained by multiplying a preconditioning matrix of the...In this paper,preconditioned gridless methods are developed for solving the threedimensional(3D)Euler equations at low Mach numbers.The preconditioned system is obtained by multiplying a preconditioning matrix of the type of Weiss and Smith to the time derivative of the 3D Euler equations,which are discretized under the clouds of points distributed in the computational domain by using a gridless technique.The implementations of the preconditioned gridless methods are mainly based on the frame of the traditional gridless method without preconditioning,which may fail to have convergence for flow simulations at low Mach numbers,therefore the modifications corresponding to the affected terms of preconditioning are mainly addressed in the paper.An explicit four-stage Runge–Kutta scheme is first applied for time integration,and the lower-upper symmetric Gauss-Seidel(LU-SGS)algorithm is then introduced to form the implicit counterpart to have the further speed up of the convergence.Both the resulting explicit and implicit preconditioned gridless methods are validated by simulating flows over two academic bodies like sphere or hemispherical headform,and transonic and nearly incompressible flows over one aerodynamic ONERA M6 wing.The gridless clouds of both regular and irregular points are used in the simulations,which demonstrates the ability of the method presented for coping with flows over complicated aerodynamic geometries.Numerical results of surface pressure distributions agree well with available experimental data or simulated solutions in the literature.The numerical results also show that the preconditioned gridless methods presented still functions for compressible transonic flow simulations and additionally,for nearly incompressible flow simulations at low Mach numbers as well.The convergence of the implicit preconditioned gridless method,as expected,is much faster than its explicit counterpart.展开更多
A quadtree-based adaptive Cartesian grid generator and flow solver were developed. The grid adaptation based on pressure or density gradient was performed and a gridless method based on the least-square fashion was us...A quadtree-based adaptive Cartesian grid generator and flow solver were developed. The grid adaptation based on pressure or density gradient was performed and a gridless method based on the least-square fashion was used to treat the wall surface boundary condition, which is generally difficult to be handled for the common Cartesian grid. First, to validate the technique of grid adaptation, the benchmarks over a forward-facing step and double Mach reflection were computed. Second, the flows over the NACA 0012 airfoil and a two-element airfoil were calculated to validate the developed gridless method. The computational results indi- cate the developed method is reasonable for complex flows.展开更多
基金Supported by the National Natural Science Foundation of China(11172134)the Funding of Jiangsu Innovation Program for Graduate Education(CXZZ110192)the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘A hybrid Cartesian grid/gridless method is developed for calculating viscous flows over multi-element airfoils.The method adopts an unstructured Cartesian grid to cover most areas of the computational domain and leaves only small region adjacent to the aerodynamic bodies to be filled with the cloud of points used in the gridless methods,which results in a better combination of the computational efficiency of the Cartesian grid and the flexibility of the gridless method in handling complex geometries.The clouds of points in the local gridless region are implemented in an anisotropic way according to the features of the thin boundary layer of the viscous flows over the airfoils,and the clouds of points at the vicinity of the interface between the grid and the gridless regions are also controlled by using an adaptive refinement technique during the generation of the unstructured Cartesian grid.An implementation of the resulting hybrid method is presented for solving two-dimensional compressible Navier-Stokes(NS)equations.The simulations of the viscous flows over a RAE2822airfoil or a two-element airfoil are successfully carried out,and the obtained results agree well with the available experimental data.
基金supported by the National Natural Science Foundation of China(No.11172134)
文摘A preconditioned gridless method is developed for solving the Euler equations at low Mach numbers.The preconditioned system in a conservation form is obtained by multiplying apreconditioning matrix of the type of Weiss and Smith to the time derivative of the Euler equations,which are discretized using agridless technique wherein the physical domain is distributed by clouds of points.The implementation of the preconditioned gridless method is mainly based on the frame of the traditional gridless method without preconditioning,which may fail to converge for low Mach number simulations.Therefore,the modifications corresponding to the affected terms of preconditioning are mainly addressed.The numerical results show that the preconditioned gridless method still functions for compressible transonic flow simulations and additionally,for nearly incompressible flow simulations at low Mach numbers as well.The paper ends with the nearly incompressible flow over a multi-element airfoil,which demonstrates the ability of the method presented for treating flows over complicated geometries.
文摘The least-square gridless method was extended to simulate the compressible multi-material flows. The algorithm was accomplished to solve the Arbitrary Lagrange-Euler( ALE) formulation. The local least-square curve fits was adopted to approximate the spatial derivatives of a point on the base of the points in its circular support domain,and the basis function was linear. The HLLC( Harten-Lax-van Leer-Contact) scheme was used to calculate the inviscid flux. On the material interfaces,the gridless points were endued with a dual definition corresponding to different materials. The moving velocity of the interface points was updated by solving the Riemann problem. The interface boundary condition was built by using the Ghost Fluid Method( GFM).Computations were performed for several one and two dimensional typical examples. The numerical results show that the interface and the shock wave are well captured,which proves the effectiveness of gridless method in dealing with multi-material flow problems.
文摘The gridless method coupled with finite rate chemistry model is employed to simulate the external combustion flow fields of M864 base bleed projectile. The fluid dynamics process is described by Euler Equation in 2-D axisymmetric coordinate. The numerical method is based on least-square gridless method,and the inviscid flux is calculated by multi-component HLLC( Harten-Lax-van Leer-Contact) scheme,and a H2-CO reaction mechanism involving 9 species and 11 reactions is used. The computations are performed for the full projectile configuration of Ma = 1. 5,2,and 3. The hot air injection cases and inert cases are simulated for comparison. The numerical results show that due to the combustion in the weak region,the recirculation zone enlarges and moves downstream,the base pressure increases and the total drag force coefficient decreases. At Ma = 3. 0,the rear stagnation point shifts downstream approximate 0. 26 caliber,and the base pressure increases about 53. 4%,and the total drag force coefficient decreases to 0. 182 which agrees well with the trajectory model prediction. Due to neglecting the effects of viscosity and turbulence,there exists a certain difference at Ma = 1. 5,2. 0.
基金This work was supported in part by National Natural Science Foundation of China(No.11972189)Natural Science Foundation of Jiangsu Province(No.BK20190391).
文摘In this paper,preconditioned gridless methods are developed for solving the threedimensional(3D)Euler equations at low Mach numbers.The preconditioned system is obtained by multiplying a preconditioning matrix of the type of Weiss and Smith to the time derivative of the 3D Euler equations,which are discretized under the clouds of points distributed in the computational domain by using a gridless technique.The implementations of the preconditioned gridless methods are mainly based on the frame of the traditional gridless method without preconditioning,which may fail to have convergence for flow simulations at low Mach numbers,therefore the modifications corresponding to the affected terms of preconditioning are mainly addressed in the paper.An explicit four-stage Runge–Kutta scheme is first applied for time integration,and the lower-upper symmetric Gauss-Seidel(LU-SGS)algorithm is then introduced to form the implicit counterpart to have the further speed up of the convergence.Both the resulting explicit and implicit preconditioned gridless methods are validated by simulating flows over two academic bodies like sphere or hemispherical headform,and transonic and nearly incompressible flows over one aerodynamic ONERA M6 wing.The gridless clouds of both regular and irregular points are used in the simulations,which demonstrates the ability of the method presented for coping with flows over complicated aerodynamic geometries.Numerical results of surface pressure distributions agree well with available experimental data or simulated solutions in the literature.The numerical results also show that the preconditioned gridless methods presented still functions for compressible transonic flow simulations and additionally,for nearly incompressible flow simulations at low Mach numbers as well.The convergence of the implicit preconditioned gridless method,as expected,is much faster than its explicit counterpart.
基金supported by the National Natural Science Foundation of China (10672168)
文摘A quadtree-based adaptive Cartesian grid generator and flow solver were developed. The grid adaptation based on pressure or density gradient was performed and a gridless method based on the least-square fashion was used to treat the wall surface boundary condition, which is generally difficult to be handled for the common Cartesian grid. First, to validate the technique of grid adaptation, the benchmarks over a forward-facing step and double Mach reflection were computed. Second, the flows over the NACA 0012 airfoil and a two-element airfoil were calculated to validate the developed gridless method. The computational results indi- cate the developed method is reasonable for complex flows.
